I have a 12 hours transit at Amsterdam Schiphol airport but I have no visa to exit the airport, and all hotels inside are fully booked. Shops and restaurants are all closed by the time I arrive at the airport. Are there areas to relax and get some sleep? What else is there to do inside?
I suppose by this time OP has already finished his/her layover. For future visitors, here's another suggestion: Visit the Rijksmuseum at Schiphol at no charge! It is open daily from 6:00 – 20:00 and is located between piers E and F.
Also see this list:
I recently traveled through Schiphol and there are plenty of comfortable seating areas (well padded couches) and lots of power points so you should be very comfortable.
The specific area I had in mind was next to departures gate E08.
There are also automated relax/massage chairs that operate by coin which you can use to time out for a while.
There are 24 hours food and beverage shops, but strangely available in arrivals and not departure.
There are also meditation areas where you can go to relax (although I am not sure if these are open 24 hours).
So you should easily be able to spend 12 hours.
When I had a long layover at Schiphol I found the airport park a nice place to kill some time. In particular you can actually get outside and have some fresh air, if the weather is nice.